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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.avvm.01

 Input Form

 Hypergeometric2F1[-(6/5), 4, 24/5, -z] == (1/(9765625 z^(19/5))) (399 (-1)^(1/5) (12 (-1)^(4/5) (1 + z)^2 (-42 + 99 z - 176 z^2 + 308 z^3) Log[1 + z^(1/5)] + 12 (1 + z)^2 (-42 + 99 z - 176 z^2 + 308 z^3) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (12 (1 + z)^2 (-42 + 99 z - 176 z^2 + 308 z^3) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-12 (1 + z)^2 (-42 + 99 z - 176 z^2 + 308 z^3) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (126 - 101 z + 116 z^2 + 4664 z^3 + 3696 z^4) + 12 (1 + z)^2 (-42 + 99 z - 176 z^2 + 308 z^3) Log[1 + (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( - 6 5 , 4 ; 24 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["6", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["24", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 9765625 z 19 / 5 ( 399 - 1 5 ( 12 ( - 1 ) 4 / 5 ( 308 z 3 - 176 z 2 + 99 z - 42 ) log ( z 5 + 1 ) ( z + 1 ) 2 + 12 ( 308 z 3 - 176 z 2 + 99 z - 42 ) log ( 1 - - 1 5 z 5 ) ( z + 1 ) 2 - - 1 5 ( 12 ( 308 z 3 - 176 z 2 + 99 z - 42 ) log ( ( - 1 ) 2 / 5 z 5 + 1 ) ( z + 1 ) 2 + - 1 5 ( - 1 5 ( 12 ( 308 z 3 - 176 z 2 + 99 z - 42 ) log ( ( - 1 ) 4 / 5 z 5 + 1 ) ( z + 1 ) 2 + 5 - 1 5 z 4 / 5 ( 3696 z 4 + 4664 z 3 + 116 z 2 - 101 z + 126 ) ) - 12 ( z + 1 ) 2 ( 308 z 3 - 176 z 2 + 99 z - 42 ) log ( 1 - ( - 1 ) 3 / 5 z 5 ) ) ) ) ) HypergeometricPFQ -1 6 5 4 24 5 -1 z 1 9765625 z 19 5 -1 399 -1 1 5 12 -1 4 5 308 z 3 -1 176 z 2 99 z -42 z 1 5 1 z 1 2 12 308 z 3 -1 176 z 2 99 z -42 1 -1 -1 1 5 z 1 5 z 1 2 -1 -1 1 5 12 308 z 3 -1 176 z 2 99 z -42 -1 2 5 z 1 5 1 z 1 2 -1 1 5 -1 1 5 12 308 z 3 -1 176 z 2 99 z -42 -1 4 5 z 1 5 1 z 1 2 5 -1 1 5 z 4 5 3696 z 4 4664 z 3 116 z 2 -1 101 z 126 -1 12 z 1 2 308 z 3 -1 176 z 2 99 z -42 1 -1 -1 3 5 z 1 5 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02